# Impedance and Gain Problem

#### moliver777

Joined Aug 13, 2007
2
Hi people. I'm having difficulty finding the forumulae to work out this problem which is part of a large c programming project due next week. Not knowing how this problem works is hindering my progress a lot... Any solutions/insight would be a MASSIVE help. Thanks.

Here's the problem:
A system is made up of a number of Elements (picture below represents a single element) that are modelled as 2-port networks. They are connected in series. Each element is characterised by three values; input impedance (Zi), output impedance (Zo) and gain in dB (GVi). I need to know the formula or theory behind calculating the overall system's input impedance, output impedance, and end-to-end gain taking into account all gains and coupling losses. (What the hell are coupling losses!?)

#### spar59

Joined Aug 4, 2007
57
If the systems are represented as shown i.e. simply input impedance, output impedance and an ideal amplifier of gain G then the only coupling losses are the power losses within the input and output impedances.

If the ideal amplifier outputs a certain voltage not all that voltage will appear at the input to the next stage due to the voltage drop in the output impedance.

From ohms law:-
It will in fact be (V * Input impedance of next stage) / (Input impedance of next stage + Output impedance of this stage).

i.e.
Output current of stage 1 = Output V of stage 1 / (Input impedance of stage 2 + Output impedance of stage 1).

Due to series circuit Input current of stage 2 = Output current of stage 1.

Input voltage = Input current * input impedance

Steve.